完美就座 I

固定最年轻者的位置后，剩余 6 人有 $6!$ 种排列。

其中只有 2 种为年龄递增（顺时针或逆时针）。因此概率为

$$\frac{2}{6!}=\frac{1}{360}.$$

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Original Explanation

Seat the youngest person at the table in any spot. There are $6!$ ways to arrange the remaining $6$ people that have not been seated at the table. Of those arrangements, exactly $2$ of them are in increasing order of age. Namely, these occur when they are increasing in age clockwise or counter-clockwise. Therefore, $2$ of these $6!$ equally likely permutations are in increasing order of age, so our result is $\dfrac{2}{6!} = \dfrac{1}{360}$.